Abstract
We consider the Allen-Cahn equation where Ω = B1(0) is the unit ball in ℝn and ε > 0 is a small parameter. We prove the existence SN of a radial solution uε having N interfaces {uε(r)=0} = {n-ary union}Nj=1, where 1> rε1 > rε2 >...> rεN are such that 1-rε1 ~ε log(1/ε) and rεj-1 - rεj ~ ε log(1/ε) for j = 2,..., N. Moreover, the Morse index of uε in H1r (Ωε) is exactly N.
Original language | English (US) |
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Pages (from-to) | 447-468 |
Number of pages | 22 |
Journal | Pacific Journal of Mathematics |
Volume | 229 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2007 |
Keywords
- Allen-Cahn equation
- Boundary clustered interfaces